Why do academics tend to be reluctant to ask for help from other academics?
I have never been fully immune from this kind of behavior, though I've suffered less from it than others, a fact that most likely helped me land two really nice jobs. Let me survey a few reasons why I think it happens.
Note: I'm talking of mathematics, where "robustness" is not a thing, and talking to someone does not "contaminate" your thinking (unless you are really careless).
Bob and Charlie are too proud. They don't want to be seen asking possibly stupid questions in writing.
Charlie feels that he doesn't know enough to even pose a good question, and Bob doesn't care enough. (Students generally tend to have trouble gauging their level, and I have occasionally blundered into conversations I wasn't prepared for by asking a too-advanced question.)
Bob and Charlie have seen their questions ignored too often. (My personal experience is that the usefulness of emailing an author about a paper they wrote declines sharply with the age of the paper. If the paper is 15+ years old, they most likely don't remember anything and have the same perspective as any other reader.)
Bob and Charlie don't want anyone to know they are reading the paper, as they are worried of creating expectations. (This sometimes does happen -- in that an author takes a question as a stronger sign of interest than it was intended. Though it does not appear to be a big deal, but more of an awkward moment.)
Bob and Charlie are worried Alice will view their question as a personal attack or at least as a threat. (In my career of reporting errors, this has happened 1-2 times out of somewhere near 50. But this sort of risk aversion isn't exactly out of character for much of academia...)
Bob and Charlie are not only looking to know the result or to verify it; they are also interested in understanding and having insight into the result, possibly with the goal of extending it.
If Charlie understands the result the same way Alice understands it, then Charlie is unlikely to have any insights into extending the result other than the insights that Alice has. Hence, Charlie's goal is to develop independent understanding of the result which is different from Alice's understanding.
If Charlie just asks Alice, then Charlie will now have the same understanding that Alice has (only to an inferior degree), and hence will have difficulty extending the result in directions Alice didn't think about.
If everyone did it...
Imagine getting an email every time someone doesn't know how to proceed from A to B in one of your papers. Imagine answering each of those emails, every time.
Imagine learning exactly how to derive B from A every time you're stuck. Now you never actually have to put effort into understanding a paper anymore. Say you start out asking for help every time you don't understand it if you didn't get it in a day. Everyone is always happy to answer you, you ask every time you don't get it. What's very likely going to happen is that you start sending the email earlier and earlier...
Academics are good at what they're doing. They probably got there by being stubborn at trying.
Finally, I remember reading (but I forgot where) that one of the best predictors of mathematical skill is the amount of time you're willing to spend on a problem before you give up. Assuming that the average population of academia ranks decently high on mathematical skill, you'd expect them ot be more stubborn than the average person at solving problems.